Chicago defines a common noun as: “the generic name of one item in a class or group,” noting it isn’t capitalized unless it appears in a title or starts a sentence. Chicago defines a proper noun as: “the specific name of a person, place, or thing … or the title of a work.” It is always capitalized. In its capitalization entry, AP likewise notes to “capitalize nouns that constitute the unique identification for a specific person, place, or thing.” (There is a typo here, by the way: Notice AP’s use of a serial comma?)
So, as far as animals go, cat, dog, bird, and so on are lowercase because they name a group of animals. But, I should capitalize my dogs’ names, Martin and Louis, because those are their specific names.
But what if I wanted to note what breeds my dogs are? They are both mutts. More specifically, we guess that Martin is a coonhound/boxer mix, and Louis is a chow chow/Labrador retriever mix. How did I know how to capitalize versus lowercase those breeds?
Like nouns, adjectives can be proper. Chicago defines a proper adjective as “one that, being derived from a proper name, always begins with a capital letter.” However, Chicago recommends lowercasing such words in instances when used with a “nonliteral” meaning. For example, roman numerals. Likewise, AP notes to “lowercase words that are derived from a proper noun but no longer depend on it for their meaning.” For example, venetian blind.
However, both style guides’ recommendations change for breeds and species of plants and animals. Chicago refers to these as “common names,” and notes to capitalize proper nouns and adjectives. Under its animals entry, AP has specific recommendations for breed names: “capitalize words derived from proper nouns; use lowercase elsewhere.” Both guides direct readers to particular dictionaries when in doubt.
Going back to the second graders’ animals, they were correct in that all are indeed common nouns, despite the fact that some include proper adjectives in their names. But the capitalization for each is Siamese cat, Maine coon, great white shark, and golden retriever, respectively.
In case anyone ever asks you, here are some additional examples:
Caribbean reef shark
 University of Chicago Press, The Chicago Manual of Style, 16th ed. (London: University of Chicago Press, 2010), 5.5, 204.
 Ibid., 204.
 Associated Press, The Associated Press Stylebook 2015 (New York, Associated Press: 2015), 40.
 Chicago Manual of Style, 5.67, 222.
 Ibid., 8.60, 411.
 Associated Press Stylebook, 41.
 Chicago Manual of Style, 8.127 and 8.128, 440.
 Associated Press Stylebook, 16.
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